Contents -- Preface -- Part 1 Theory -- 1. The Classical Yang-Mills Action -- 1.1 Historic Remarks -- 1.2 The Semisimple Lie Group SU(N) (N ≥ 2) -- 1.3 Gauge Connection Aµ and its Field Strength Fµν -- 1.4 Gauge-Invariant Objects -- 1.4.1 Action density and energy-momentum tensor -- 1.4.2 Nonlocal objects -- 1.5 Spontaneous Gauge-Symmetry Breaking -- 1.6 Homotopy Groups: Concept and Use -- Problems -- References -- 2. The Perturbative Approach at Zero Temperature -- 2.1 General Remarks -- 2.2 Gauge Fixing in the Functional Integration -- 2.3 One-loop Running of the Gauge Coupling -- 2.3.1 Feynman rules -- 2.3.2 Callan-Symanzik equation -- 2.3.3 Computation of the β function -- Problems -- References -- 3. Aspects of Finite-Temperature Field Theory -- 3.1 Free-Particle Partition Function: Real Scalar Field -- 3.1.1 Euclidean formulation of thermal field theory -- 3.1.2 "Rotation" to real time -- 3.2 Perturbative Loop Expansion in Thermal Gauge Theory -- 3.3 Electric Center Symmetry -- 3.3.1 Polyakov loop: Definition -- 3.3.2 Polyakov loop as an order parameter -- Problems -- References -- 4. Selfdual Field Configurations -- 4.1 The BPST Instanton and Multiinstanton Generalization -- 4.1.1 Chern-Simons current and Bogomoln'yi decomposition -- 4.1.2 Instanton in regular gauge -- 4.1.3 Singular gauge and multiinstantons -- 4.2 Sketch of the ADHM-Nahm Construction -- 4.2.1 All charge-k instantons on R4 -- 4.2.2 The 't Hooft-Polyakov monopole -- 4.2.3 Nahm's duality transformation -- 4.3 SU(2) Calorons with k = ±1 -- 4.3.1 Trivial holonomy -- 4.3.2 Nontrivial holonomy -- 4.4 One-loop Quantum Weights of Calorons -- 4.4.1 Harrington-Shepard solution -- 4.4.2 Lee-Lu-Kraan-van Baal solution -- Problems -- References -- 5. The Deconfining Phase -- 5.1 Deconfining Thermal Ground State.

5.1.1 Two principles imposed by infinite volume Yang-Mills thermodynamics -- 5.1.2 Coarse-graining and BPS saturation -- 5.1.3 Inert adjoint scalar field: Phase -- 5.1.4 Inert adjoint scalar field: Modulus and potential -- 5.1.5 Effective action and a priori estimate of thermal ground state -- 5.2 Free Thermal Quasiparticles -- 5.2.1 Quasiparticle spectrum, propagators, and momentum constraints -- 5.2.2 Pressure and energy density of noninteracting excitations -- 5.2.3 Evolution of effective gauge coupling -- 5.2.4 Trace anomaly of energy-momentum tensor -- 5.2.5 Fundamental versus effective gauge coupling -- 5.3 Effective Radiative Corrections -- 5.3.1 Loop expansion: General considerations -- 5.3.2 Feynman rules in unitary-Coulomb gauge -- 5.3.3 Loop expansion: Conjecture on its termination -- 5.3.3.1 Pinch singularities -- 5.3.3.2 Loop integration variables versus constraints -- 5.3.3.3 Two examples -- 5.3.3.4 Conclusions -- 5.3.4 Two-loop corrections to the pressure -- 5.3.4.1 General considerations -- 5.3.4.2 Calculation -- 5.3.5 Pressure: Three-loop estimates -- 5.3.6 Summary: Loop expansion of pressure -- 5.3.7 One-loop polarization tensor of the massless mode -- 5.3.7.1 General considerations -- 5.3.7.2 Prerequistes -- 5.3.7.3 Calculation of G for p2 = 0 -- 5.3.7.4 Results and discussion: G at p2 = 0 -- 5.3.7.5 Calculation of G at p2 = G -- 5.3.7.6 Propagation of longitudinal modes -- 5.4 Stable, Screened Magnetic Monopoles -- 5.4.1 Remarks on screening of static magnetic charge -- 5.4.2 Monopole density, monopole-antimonopole distance, and screening length -- 5.4.3 Area law for spatial Wilson loop? -- 5.4.4 Spatial Wilson loop in effective variables -- 5.4.4.1 Generalities on spatial Wilson loop in the effective theory -- 5.4.4.2 Part due to tree-level massive modes -- 5.4.4.3 Thermal part due to massless mode.

5.4.4.4 Quantum part due to massless mode -- 5.4.4.5 Summary of results for effective spatial Wilson -- 5.4.5 Improved ground state estimate by thermal resummation -- 5.5 Thermomagnetic Effect -- 5.5.1 Adiabatic approximation -- 5.5.2 Minkowskian Yang-Mills equations for static fields in unitary gauge -- 5.5.3 Simple static configurations with a U(1) magnetic field -- 5.5.4 Profiles -- Problems -- References -- 6. The Preconfining Phase -- 6.1 Condensation of Magnetic Monopole-Antimonopole Pairs -- 6.1.1 Geometric considerations -- 6.1.2 Derivation of the phases of macroscopic complex scalar fields -- 6.1.3 Onset of monopole condensation -- 6.1.4 Coarse-grained and free monopoles: BPS saturation and Euler-Langrange -- 6.2 The Dual Gauge Field -- 6.2.1 Effective action for the preconfining phase and thermal ground state -- 6.2.2 Free quasiparticle excitations, scale matching, and running magnetic coupling -- 6.2.3 Supercooling -- 6.3 Abrikosov-Nielsen-Olesen (ANO) Vortex Lines and Center-Vortex Loops -- 6.3.1 ANO vortex in the Abelian Higgs model -- Problems -- References -- 7. The Confining Phase -- 7.1 Decay of the Preconfining Ground State -- 7.1.1 The center-vortex condensate -- 7.1.2 Real-time relaxation of to zero energy density and pressure -- 7.1.3 Multiplicity of center-vortex loops with n selfintersections -- 7.2 Nonthermal Pressure -- 7.2.1 Naive thermodynamical estimate -- 7.2.2 Borel resummation and analytic continuation -- 7.3 Evolving Center-Vortex Loops -- 7.3.1 The case of n = 0: Mass gap -- 7.3.2 The case of n = 1: Emergence of order -- Problems -- References -- Part 2 Applications -- 8. The Approach of Thermal Lattice Gauge Theory -- 8.1 Pressure, Energy Density, and Entropy Density -- 8.2 Differential versus Integral Method: Thermodynamical Quantities -- 8.3 Analytical Aspects of Thermal Lattice Gauge Theory.

8.3.1 Identification of relevant field configurations -- 8.3.2 Lattice manifestation of φ and spatial Wilson loop -- 8.3.3 Where is the preconfining phase? -- References -- 9. Black-Body Anomaly -- 9.1 Introduction -- 9.2 The Cosmic Microwave Background (CMB) -- 9.2.1 Historical remarks and results of CMB explorations -- 9.3 SU(2)CMB and Thermal Photon Propagation -- 9.3.1 Modified dispersion law and spectral energy density -- 9.4 Determination of Tc -- 9.4.1 Very weak evidence for Tc 2.73 K: Extragalactic magnetic fields -- 9.4.2 Weak evidence for Tc 2.73 K: Cold clouds of dilute atomic hydrogen within the Milky Way -- 9.4.3 Evidence for Tc 2.73 K: CMB at very low frequencies -- 9.4.3.1 Arcade 2 and earlier radio frequency surveys of the CMB -- 9.4.3.2 Evanescent CMB photons at low frequencies -- 9.4.3.3 Thermodynamical decoupling: Coexistence of several temperatures -- 9.5 Laboratory Experiment on Black-Body Anomaly -- 9.5.1 Bolometry and radiometry of SU(2) photons -- 9.5.2 Preparation of a U(1) black-body cavity at low temperatures -- 9.5.3 Wave-guide loads to detect the black-body anomaly? -- References -- 10. Astrophysical and Cosmological Implications of SU(2)CMB -- 10.1 Cold and Dilute Clouds of Atomic Hydrogen -- 10.1.1 Two-point correlation of energy density in thermal U(1) gauge theory -- 10.1.1.1 General strategy -- 10.1.1.2 Decomposition into thermal and vacuum parts -- 10.1.1.3 Results -- 10.1.2 The case of deconfining thermal SU(2) gauge theory -- 10.1.2.1 Radiative modification of dispersion law for massless mode -- 10.1.2.2 Thermal part of two-point correlation -- 10.1.2.3 Estimate for vacuum part of two-point correlation -- 10.1.2.4 Numerical results -- 10.1.3 Stability of clouds of atomic hydrogen in the Milky Way -- 10.2 Large-angle Anomalies of the CMB -- 10.2.1 Temperature as a scalar field.

10.2.2 Temperature fluctuations and background cosmology -- 10.2.3 Dynamic component in the cosmic dipole: Numerical analysis -- 10.2.3.1 Principle remarks and boundary conditions -- 10.2.3.2 Results -- 10.2.4 Alignment and suppression of low multipoles? -- 10.3 Planck-scale Axion and Dark Energy -- 10.3.1 Model of the very early universe -- 10.3.2 Planck-scale axion: Cosmological evolution after CMB decoupling -- 10.3.2.1 Cosmological evolution from zdec = 1089 to z = 0 -- 10.3.2.2 Massive CMB photons in the future -- 10.3.2.3 Slowly rolling Planck-scale axion: Dark energy and dark matter? -- References -- Acknowledgments -- Author Index -- Subject Index.